Additive manufacturing is a technique for building a three-dimensional object from a mathematical model of the object. In the additive manufacturing technique called fused-deposition modeling, the object is built by feeding a thermoplastic filament into a heated extrusion head. The heated extrusion head melts and deposits the molten thermoplastic material as one or more runs of material. Typically, a run of material is shaped like a thread or like the toothpaste that is squeezed from a tube but much smaller. When a run is deposited, it is just slightly above its melting point. After it is deposited, the run quickly solidifies and fuses with the runs that it touches.
Perhaps the greatest advantage of additive manufacturing is that it can build an object of any shape. To accomplish this, however, there are constraints on the sequence in which the runs can be deposited. First, each run must be supported. In other words, a run cannot be deposited on air. Therefore, each run must be deposited on:                (i) a platform that is not part of the object, or        (ii) one or more previously-deposited runs that will be part of the object, or        (iii) a temporary scaffold of support material that is not part of the object, or        (iv) any combination of i, ii, and iii.Second, when a three-dimensional surface is sealed, it is no longer possible to deposit a run inside of that surface. This is analogous to the situation in which once you close a box, you can't put anything into the box.        
There is a general methodology that is used in additive manufacturing that satisfies these constraints and enables the building of an object of any shape. The three-dimensional model of the object is modeled as thousands of thin horizontal layers. Each layer is modeled as thousands of runs and voids. The object is then built, one run at a time, one layer at a time, only in the +Z direction.
There are, however, costs and disadvantages associated with traditional additive manufacturing.